Solve (frac{15x^{3}y-60x^{2}y}{3x^{2}y+15xy})(frac{18x^{2}y+90xy}{3x^3y^2-12x^2y^2})

$$( \frac { 15 x ^ { 3 } y - 60 x ^ { 2 } y } { 3 x ^ { 2 } y + 15 x y } ) ( \frac { 18 x ^ { 2 } y + 90 x y } { 3 x ^ { 3 } y ^ { 2 } - 12 x ^ { 2 } y ^ { 2 } } )$$

Evaluate

$$\frac{30}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{15x^{3}y-60x^{2}y}{3x^{2}y+15xy}.

$$\frac{15y\left(x-4\right)x^{2}}{3xy\left(x+5\right)}\times \frac{18x^{2}y+90xy}{3x^{3}y^{2}-12x^{2}y^{2}}$$

Cancel out 3xy in both numerator and denominator.

$$\frac{5x\left(x-4\right)}{x+5}\times \frac{18x^{2}y+90xy}{3x^{3}y^{2}-12x^{2}y^{2}}$$

Factor the expressions that are not already factored in \frac{18x^{2}y+90xy}{3x^{3}y^{2}-12x^{2}y^{2}}.

$$\frac{5x\left(x-4\right)}{x+5}\times \frac{18xy\left(x+5\right)}{3\left(x-4\right)x^{2}y^{2}}$$

Cancel out 3xy in both numerator and denominator.

$$\frac{5x\left(x-4\right)}{x+5}\times \frac{6\left(x+5\right)}{xy\left(x-4\right)}$$

Multiply \frac{5x\left(x-4\right)}{x+5} times \frac{6\left(x+5\right)}{xy\left(x-4\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5x\left(x-4\right)\times 6\left(x+5\right)}{\left(x+5\right)xy\left(x-4\right)}$$

Cancel out x\left(x-4\right)\left(x+5\right) in both numerator and denominator.

$$\frac{5\times 6}{y}$$

Multiply 5 and 6 to get 30.

$$\frac{30}{y}$$

Expand

$$\frac{30}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{15x^{3}y-60x^{2}y}{3x^{2}y+15xy}.

$$\frac{15y\left(x-4\right)x^{2}}{3xy\left(x+5\right)}\times \frac{18x^{2}y+90xy}{3x^{3}y^{2}-12x^{2}y^{2}}$$

Cancel out 3xy in both numerator and denominator.

$$\frac{5x\left(x-4\right)}{x+5}\times \frac{18x^{2}y+90xy}{3x^{3}y^{2}-12x^{2}y^{2}}$$

Factor the expressions that are not already factored in \frac{18x^{2}y+90xy}{3x^{3}y^{2}-12x^{2}y^{2}}.

$$\frac{5x\left(x-4\right)}{x+5}\times \frac{18xy\left(x+5\right)}{3\left(x-4\right)x^{2}y^{2}}$$

Cancel out 3xy in both numerator and denominator.

$$\frac{5x\left(x-4\right)}{x+5}\times \frac{6\left(x+5\right)}{xy\left(x-4\right)}$$

Multiply \frac{5x\left(x-4\right)}{x+5} times \frac{6\left(x+5\right)}{xy\left(x-4\right)} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5x\left(x-4\right)\times 6\left(x+5\right)}{\left(x+5\right)xy\left(x-4\right)}$$

Cancel out x\left(x-4\right)\left(x+5\right) in both numerator and denominator.

$$\frac{5\times 6}{y}$$

Multiply 5 and 6 to get 30.

$$\frac{30}{y}$$